# Median

© Paul Cooijmans

## Explanation

This is the middle score, when the scores are ranked from highest to lowest. When the number of scores is even it is the mean of the middle two scores (but when the middle two scores are some distance apart, logically all of the missing but possible scores therebetween are median scores). It divides the test population in two equal parts. It is the simplest form of quantile; other quantiles are those that divide the population in three, four, five, etcetera parts. Best known are centiles. Note that quantiles are the points that divide the population, and not the intervals or slots *between* those points, as is often thought. Also, the number of quantiles, or which are the highest and lowest, is open to some debate. The highest centile is mostly thought to be 99; however, the 100^{th} centile really belongs to any score that is higher the highest score in the sample, and the 0^{th} to any score that is lower than the lowest.

The median is an indicator of central tendency or average, and particularly useful on non-linear scales or with non-normal distributions; other such indicators are the arithmetic mean (best used on linear scales and with normal distributions), and the mode (most occurring score, especially meaningful in strongly skewed distributions). With raw psychometric data, the median is usually the most appropriate choice of average, the arithmetic mean, although better known, coming in vogue only after normalization of the distribution or otherwise converting the data to a scale approximating linearity and normality.